13 citations · 75 across the 82 of their papers we have counts for
35 papers · 1 filter
On Series Involving Cubed Catalan Numbers
Kunle Adegoke
Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a fa…
Three combinatorial sums involving central binomial coefficients
Kunle Adegoke, Robert Frontczak
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In…
New harmonic number series
Kunle Adegoke, Robert Frontczak
Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inv…
Combinatorial identities with multiple harmonic-like numbers
Kunle Adegoke, Robert Frontczak
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters.…
Evaluation of some alternating series involving the binomial coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
We evaluate in closed form several alternating infinite series involving the binomial coefficients and in the denominator. One of our results generalizes…
Fibonacci Identities via Fibonacci Functions
Kunle Adegoke
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and hav…
Fibonacci sums and divisibility properties
Kunle Adegoke, Robert Frontczak
Based on a variant of Sury's polynomial identity we derive new expressions for various finite Fibonacci (Lucas) sums. We extend the results to Fibonacci and Chebyshev polynomials,…
A series of Ramanujan, two-term dilogarithm identities and some Lucas series
Kunle Adegoke, Robert Frontczak
We study an elementary series that can be considered a relative of a series studied by Ramanujan in Part 1 of his Lost Notebooks. We derive a closed form for this series in terms o…
Golden Ratio Base Expansions of the Logarithm and Inverse Tangent of Fibonacci and Lucas Numbers
Kunle Adegoke, Jaume Oliver Lafont
Let , the golden ratio, and . Let and be the Fibonacci and Lucas numbers, defined by and $L_n=α^n + β^…
Multiple sums involving the terms of a general second order sequence of numbers
Kunle Adegoke
We evaluate the nested sum where and are any integers and…
Fibonacci Identities Involving Reciprocals of Binomial Coefficients
Kunle Adegoke
We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.
Fibonacci-Zeta infinite series associated with the polygamma functions
Kunle Adegoke, Sourangshu Ghosh
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the…
Relating certain weighted Fibonacci series to Bernoulli polynomials via the polylogarithm function
Kunle Adegoke
We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of…
Generalizations of Fibonacci-Lucas inverse tangent summation identities of Hoggatt and Ruggels
Kunle Adegoke
We derive generalizations of a couple of inverse tangent summation identities involving Fibonacci and Lucas numbers. As byproducts we establish many new inverse tangent identities…
Basic properties of a generalized third order sequence of numbers
Kunle Adegoke
We study the properties of the third order sequence defined by the recurrence relation $w_n = rw_{n - 1} + sw_{n - 2} + tw_{n - 3}\, (n \ge…
A master identity for Horadam numbers
Kunle Adegoke
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
Fibonacci and Lucas Identities the Golden Way
Kunle Adegoke
By expressing Fibonacci and Lucas numbers in terms of the powers of the golden ratio, and its inverse, , a multitude of Fibonacci and Lucas…
Linear Properties of Generalized -step Fibonacci Numbers
Kunle Adegoke
We present numerous interesting, mostly new, results involving the -step Fibonacci numbers and -step Lucas numbers and a generalization. Properties considered include recurre…
Weighted sums of some second-order sequences
Kunle Adegoke
We derive weighted summation identities involving the second order recurrence sequence defined by $w_0 = a,\,w_1 = b;\,w_n = pw_{n - 1} - qw_{n - 2}\…
Sums of arctangents and sums of products of arctangents
Kunle Adegoke
We present new infinite arctangent sums and infinite sums of products of arctangents. Many previously known evaluations appear as special cases of the general results derived in th…
Symmetry properties of finite sums involving generalized Fibonacci numbers
Kunle Adegoke, Oluwaseyi Oshin
We extend a result of I. J. Good and prove more symmetry properties of sums involving generalized Fibonacci numbers
Factored closed-form expressions for the sums of cubes of Fibonacci and Lucas numbers
Kunle Adegoke
We obtain explicit factored closed-form expressions for Fibonacci and Lucas sums of the form \mbox{} and \mbox{}, where $r…
Sums of fourth powers of Fibonacci and Lucas numbers
Kunle Adegoke
We obtain closed-form expressions for all sums of the form \mbox{} and \mbox{} and their alternating versions, where $F_…
Generalizations for reciprocal Fibonacci-Lucas sums of Brousseau
Kunle Adegoke
We derive closed form expressions for finite and infinite Fibonacci-Lucas sums having products of Fibonacci or Lucas numbers in the denominator of the summand. Our results generali…